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How many different 6-letter sequences are there that consist of 1A, 2B's and 3C's ?

A 6 B 60 C 120 D 360 E 720

I thought the answer is 6!/2!3! = 60

But the answer is not 60.

# of different permutations of 6 letters ABBCCC is indeed \(\frac{6!}{2!3!}=60\), so you are right answer must be B (60).

THEORY: Permutations of \(n\) things of which \(P_1\) are alike of one kind, \(P_2\) are alike of second kind, \(P_3\) are alike of third kind ... \(P_r\) are alike of \(r_{th}\) kind such that: \(P_1+P_2+P_3+..+P_r=n\) is:

\(\frac{n!}{P_1!*P_2!*P_3!*...*P_r!}\).

For example number of permutation of the letters of the word "gmatclub" is \(8!\) as there are 8 DISTINCT letters in this word.

Number of permutation of the letters of the word "google" is \(\frac{6!}{2!2!}\), as there are 6 letters out of which "g" and "o" are represented twice.

Number of permutation of 9 balls out of which 4 are red, 3 green and 2 blue, would be \(\frac{9!}{4!3!2!}\). _________________

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There is another approach as we can arrange from either A to C or C to A. So...

6C1 X 5C2 (A to C) = 60; It is equal to 6C3 X 3C2 (C to A) which has the same result.

Yup this question can be solved a couple of different ways. The easiest is obviously the permutation formula for repeating elements quoted above by Bunuel. The answer is 60, regardless of what the OA indicates.

This highlights a recurring theme on GMAT problems. You should always double check the math for yourself and not trust the material blindly. Typos happen, mistakes occur. If you understand how to solve the questions, you'll get them right on the GMAT as that material is checked, rechecked and checked again for mistakes.

Re: How many different 6-letter sequences are there that consist [#permalink]
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